Rob Bayer
Math 55 Worksheet
August 30, 2010
Instructions
•
Introduce yourselves! Despite popular belief, math is in fact a team sport!
•
Find some blackboard space, a piece of chalk, and decide who will be your ±rst scribe.
•
Do the problems below, having a di²erent person be the scribe for each one.
•
Try to work out the problems as a group, but feel free to ³ag me down if you run into a wall.
Logic Symbols and Truth Tables
1. Let
c
=“It is cloudy,”
r
=“It is raining”,
s
=“It is sunny”,
w
=“The ground is wet”,
n
= “It is night”.
Translate each of the following into English
(a)
c
→¬
s
(b)
¬
s
→
c
∨
n
(c)
r
→
w
∧
c
2. Using the same propositional variables as above, translate each of the following into formal logical statements:
(a) It is raining whenever the ground is wet.
(b) If it’s sunny, then it’s not raining.
(c) It only rains at night.
3. Create a truth table for each of the following expressions. Determine whether each is a tautology, a
contradiction, or neither.
(a) (
p
∨
q
)
∧
(
¬
p
∨
q
)
(b)
p
∨
q
p
∧
q
(c)
p
→
(
¬
p
→
q
)
(d)
¬
(
p
∧
q
)
↔¬
p
∨¬
q
Logic Puzzles
1. The island of Knights and Knaves has only two kinds of inhabitants: Knights (who always tell the truth) and
Knaves (who always lie). After being shipwrecked on the island, you decide to try to ±gure out who the
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 Summer '09
 RobBayer
 Math, Logic, following truth table, following compound propositions

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